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Q. 46

Expert-verified
Found in: Page 452

Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

Book edition 4th
Author(s) Randall D. Knight
Pages 1240 pages
ISBN 9780133942651

FIGURE P16.46 is a snapshot graph at t = 0 s of a 5.0 Hz wave traveling to the left. a. What is the wave speed? b. What is the phase constant of the wave? c. Write the displacement equation for this wave.

Part a

The wave speed is .

Part b

The phase constant of the wave is

Part c

The displacement of the wave is .

See the step by step solution

Given information

A snapshot graph at t = 0 s of a 5.0 Hz wave traveling to the left is shown below

Part a

From the history graph, it can be observed that and .

The speed of the wave is given by .

Substitute the given values

Therefore, the wave speed is .

Part b

A phase constant can be obtained by .

Thus,

The value of alone given the two values of the phase constant. One of the values will cause the displacement to start at and increases with distance while the other cause the displacement to start at and decreases with distance.

Therefore the equation of wave for is

The value rad is the phase constant for which displacement increases as increases.

Part c

The equation for the displacement of the wave is

Substitute the given values

Therefore, the displacement equation for this wave is .